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January 10, 2026Balneo and PRM Research Journal6 citationsOpen Access

Modeling Post-COVID Respiratory Rehabilitation with Nonlinear Dynamics and Fractal Metrics: Beyond Spirometry

CUClara UrsescuECE Puiu CostescuMPM D Popescu

Key Result

Post-COVID patients showed significant respiratory improvement after 8 weeks of rehabilitation, with FD increasing from 1.08 to 1.23 (p < 0.001) and FEV1 rising by 17%.

Key Points

  • Evaluate nonlinear dynamics and fractal analysis for understanding post-COVID respiratory recovery.
  • Analyzed respiratory function in adults with post-COVID symptoms and healthy controls.
  • Used spirometry, thoracic impedance, and pulse-oximetry for evaluations.
  • Applied nonlinear analytical techniques and fractal metrics in conjunction with standard clinical measures.
  • Conducted an 8-week structured rehabilitation program focusing on breathing techniques and aerobic training.
  • Fractal dimension improved significantly from 1.08 ± 0.03 to 1.23 ± 0.03 after rehabilitation (p < 0.001).
  • FEV1 increased by 17%, DLCO by 25%, and the 6MWT by 80 meters post-rehabilitation.
  • Ratings of dyspnea decreased by 40%.
  • Nonlinear attractors revealed distinct morphologies distinguishing healthy individuals from post-COVID patients.

Structured PICO

Does an 8-week respiratory rehabilitation program improve respiratory fractal dimension and clinical indices in adults with persistent post-COVID respiratory symptoms?

P
Population
Adults aged 18-75 with a documented history of SARS-CoV-2 infection and persistent respiratory symptoms lasting more than 12 weeks (n=68, at least 34 per group). Excluded: severe pulmonary conditions (COPD GOLD IV, idiopathic pulmonary fibrosis), severe cardiovascular comorbidities (NYHA class III-IV), and neurological/musculoskeletal impairments.
I
Intervention
8-week structured three-phase rehabilitation program incorporating diaphragmatic breathing, HRV-based biofeedback, and progressive aerobic training.
C
Comparator
Age- and sex-matched healthy adults with no prior COVID-19 infection and normal pulmonary function (for baseline comparison), and pre-rehabilitation baseline (for intervention effect).
O
Outcome
Higuchi's fractal dimension (HFD) of respiratory signals at 8 weeks.surrogate

An 8-week respiratory rehabilitation program significantly improved nonlinear fractal dimensions of respiratory dynamics, correlating with enhanced spirometric and functional outcomes in post-COVID patients.

Limitations

  • Many nonlinear outputs are derived from simulations rather than complete raw clinical datasets
  • Absence of full participant-level nonlinear time-series limits the ability to validate model–data agreement
  • Proposed fractal thresholds and nonlinear markers require empirical confirmation in larger, prospective cohorts
  • Single-center investigation

Abstract

COVID-19 frequently results in extended respiratory challenges that hinder daily activities and diminish quality of life. Standard pulmonary function tests (PFTs) offer significant, though partial, understanding of the intricate dynamics of post-COVID respiration. This study evaluates the integration of nonlinear dynamics and fractal analysis to characterize respiratory recovery and assess the effects of an 8-week rehabilitation program. We conducted a prospective investigation involving adults with persistent post-COVID respiratory symptoms alongside age-matched healthy controls. Respiratory function was evaluated using spirometry, thoracic impedance belts, and pulse-oximetry. Nonlinear analytical techniques - including phase-space attractor reconstruction and bifurcation analysis - were applied in combination with fractal metrics such as the Higuchi fractal dimension and box-counting. Standard clinical measures (FEV₁, FVC, DLCO, 6MWT, and dyspnea scores) were also recorded. All patients completed a structured three-phase rehabilitation program incorporating diaphragmatic breathing, HRV-based biofeedback, and progressive aerobic training. Nonlinear attractors displayed distinct morphologies: healthy individuals exhibited stable oscillations, post-COVID patients presented compressed, unstable cycles, and rehabilitation shifted trajectories towards normalization. Bifurcation diagrams illustrated essential compliance parameters that distinguish stability, collapse, and unstable respiration. The fractal dimension (FD) improved significantly from 1.08 ± 0.03 to 1.23 ± 0.03 after 8 weeks (p 1.20). Conventional indices improved concordantly: FEV1 went up by 17%, DLCO by 25%, the 6MWT by 80 meters, and ratings of dyspnea went down by 40%. Coupling nonlinear dynamics with fractal analysis provides higher-resolution assessment of respiratory recovery during post-COVID rehabilitation. Attractors, bifurcation thresholds, and fractal dimensions augment traditional metrics, capturing adaptability and stability that conventional metrics miss. These technologies can support individualized therapy progression and early identification of patients at risk for persistent dysfunction.

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Cite This Study

Ursescu et al. (2025) studied this question. Post-COVID patients showed significant respiratory improvement after 8 weeks of rehabilitation, with FD increasing from 1.08 to 1.23 (p < 0.001) and FEV1 rising by 17%.

synapsesocial.com/papers/6963221991e05aa366cb8964https://doi.org/10.12680/balneo.2025.901
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